June 26, 1865.] 



♦ KNOWLEDGE ♦ 



541 



•0000520S3, or ttJ oot^* °^ »» ^^'^^ 

 of the film of air at E C 



hence the sides about their equal anqles are proportional 

 (Euclid VI., 4), so that A D : D E ::" D E : i) B (or EC), 

 ■which is the thickness we waut. Putting tins into figures, 

 100 feet : '25 inch :: ■'25 inch : what we shall find to be 



which is the thickness 

 If, instead of air, we till the 

 space between the two surfaces with any liquid, the rings 

 diminish in radius, but preserve their proportions unaltered. 

 In this way Newton was enabled to show that the thick- 

 ness of a soap-bubble when, just before bui-sting, it exhibits 

 the black of the first order of colours, must be less than 

 •00000075 inch '. 



So far we have supposed our "Newton's rings," as they 

 are called, to be formed in ordinary daylight. If, however, 

 instead of sunlight, which is compounded of all the colours, 

 ■we employ monochromatic light, wo shall find that the 

 rings will consist alternately of black ones, and others 

 coloured by our source of illumination. Thus if we light 

 onr tangent lenses with red light, we shall have red and 

 black circles alternately exhibited round our central black 

 spot ; ■with yellow light, yellow and black ; with violet 

 light, violet and black ; and so on. But this is not all, 

 ■with red light the rings are largest ; with orange, smaller ; 

 •with yellow, smaller still ; and so ou through green, blue, 

 indigo, ^■iolet, ifcc, gradually contracting as the light 

 employed becomes more refrangible. Another notable 

 fact was brought to light by Newton's measurements. He 

 found the squares of the diametei-s of the brightest parts 

 of each ring to be in the arithmetical progresf^ion of the 

 odd numbers 1, 3, 5, 7, 9, &c., and the squares of the 

 diameters of the darkest parts in the arithmetical progres- 

 sion of the even numbers 2, i, G, 8, and 10 ; and when we 

 reflect that one of the glasses is plane, and that the 

 differences of thickness are directly referable to the equable 

 curvature of the other, it ■will be seen at once that the 

 distances between them at these rings must be in the same 

 progression when the incident white light is perpen- 

 dicular. Newton found that the thickness of the air-tilm 

 at the darkest part of the first dark ring was T^^j-iTToth of 

 an inch. By multiplying this number by the progression 

 1, 3, 5, 7, 9, ic, and by 2, 4, 6, 8, 10, he obtained the 

 resulta set fort*i in the following little table : — 



Thickness of the air at 

 the most lominotis part. 



First Bing 



Second Ring 



Third Ring 



Fonrth Bing rrsWo 



Thicknes!^ of the air at 

 the most obactlre part. 



TT^'ooo (*^^ "e ifuoo) 



Observe the significance of this. Here is proof positive 

 that something is recurring periodically, and rhythmically. 

 Newton explained the observed phenomena on his emissive 

 hypothesis (to which we have pre^nously referred Ln these 

 papers) by supposing that his material particles of light 

 had poles and rotated round axes at right angles to the 

 line joining these poles. If, then, we assume a particle to 

 arrive at one surface of a film of a particular thickness, it 

 would have just time to turn once completely round, thus 

 presenting its attractive pole to the surface of the glass 

 Tinderneath, into which it would be pulled and be lost to the 

 eye In a film twice as thick it would make two complete 

 rotations with the same result, and soon. Hence the dark 

 rings. In the case of a film of half the thickness, however, 

 the supposititious corpuscle would only have time to turn 

 half way round, would present its repulsive pole to the 

 second surface of the film, and would be reflected ; 

 the same thing happening when the film was one and 

 a-half times as thick, and so on : whence arose the bright 

 rings. Newton's not very happy phraseology in accounting 

 for the phenomena on his emissive hypothesis, describes the 



corpuscles of light as being aflfected by " fits of easy trans- 

 mission and reflection." Wo liiivo before intimated how, 

 were this hypothesis true, the velocity of light should be 

 greater in water, glass, >tc., than in air or vacuo; and that 

 the fact of light being retanlrd iu refracting media having 

 been experimentally established, Newton's conception was 

 at once shown to be baseless. Moreover, reverting to this 

 particular experiment on which we have been treating, 

 Newton's assumption was that the action of reflection or 

 transmission which formed the rings took place at a single 

 surface (the second one), whereas by destroying reflection 

 from one of the two internal surfaces bounding the film, 

 we cause every trace of the rings to vanish at once. 



CHATS ON 

 GEOMETRICAL MEASUREMENT. 



By RiciiARD A. Proctou. 

 TUE COKE. 

 (^Continued from page 480.) 

 A. "We are now to deal with the volume of a cone. 

 JI. Yes. The pi-oblem is a very simple one. As in the 

 case of a cylinder we can take a cone on any base circular, 

 elliptical, or irregular (so only, at least, that we can deter- 

 mine the area of the base) ; and the vertex of the cone may 

 have any position, so long as we know the height of 

 the cone. 



A. I suppose we use, in this case, what we determined 

 respecting the volume of pyramids ; just as we used the 

 known volume of prisms when dealing with the cylinder. 



Fig. 4. 



J/. Precisely. Suppose for instance V, Fig. 4, to be the 

 vertex of a cone on the base A B C D H, V M the height 

 of the cone. Within the curvilinear area A B D H in- 

 scribe the polygon A B C D E F . . . . having a great 

 number of sides, and join V A, \^ B, V 0, &o. Then we 

 have a pyramid A B C D . . . . V enclosed within the 

 cone A B D H V. And manifestly we can make the 

 volume of the enclosed pyramid as nearly equal as we 

 please to the volume of the enclosing cone, by taking the 

 points A, B, C, D, &c., sufficiently near to each other. For, 

 the thin slices A B V, B C V, C D V, ic, left outside the 

 pyramid will together be less than a conical shell enclosed 

 between the conical surface A B C D . . . . V, and another 

 having V as its vertex, A F as the plane of its base, and 

 touching the planes A B V, B C V, &c. ; moreover, this 

 shell may be made as thin as we please, by making the 

 sides A B, B C, D, ic, of our polygon, as short as we 

 please. 



A. Wherefore, I see, the cone A B D H V is ultimately 

 equal to the pyramid A B C D . . . . V. 



J/. Yes ; and this pyramid, since the rectilinear area 

 A B C D . . . . is ultimately equal to the curvilinear area^ 



